After the 2015 season, Manfred congratulated himself on his earlier restraint. “What I said at the beginning of the year was that, before we made a judgment and started to talk about changes, that we needed at least another year of data,” Manfred said. “Every once in awhile, even I get to be right.”

He was right: Just as it began to seem certain that only a deus ex Manfred could rescue the sport from soccer-esque scores, baseball’s offense came back from the brink. The only problem is that no one knows why, or whether it will last. To unravel the mystery, we examined the most likely suspects — warmer weather, better rookie bats and bouncier baseballs — completing our investigation by shipping a bushel of balls to a laboratory for testing.

A sudden increase in offense

Manfred’s tune changed because of what he called “a really interesting uptick in offense late in the year … a statistically significant increase in scoring.” Below is a graph of runs scored per nine innings in each regular-season month from 2000 to 2015. It shows a steep climb last August and September/October, and although it doesn’t display postseason scoring — which is typically lower than the regular-season rate — teams averaged 4.36 runs per game during the 2015 postseason, more than they had scored in any month from April through July of that year.

Thanks to that late-season surge, league-wide regular-season scoring rose from 4.07 runs per game in 2014 to 4.25 runs per game in 2015, the largest single-season spike since 2005 to 2006 and only the second year-to-year increase of any size in that span. Not only did the extended decline in baseball’s scoring stop, but offense bounced back to where it had been four years before. And over the final third of the regular season, teams produced runs at a rate higher than they had in any full season since 2009, the year before the strike zone started expanding and scoring dipped so suddenly that some observers dubbed 2010 “the year of the pitcher.”

We can’t credit last year’s increase in offense to a reversal in strike-zone size: The zone actually grew again in 2015, albeit very slightly. Similarly, strikeout and walk rates barely budged. But home runs rebounded by enough to produce most of the extra scoring. The graph below shows monthly home-run rates as a percentage of contact (HR/Contact), where “contact” is defined as at-bats minus strikeouts. Once again, playoff rates aren’t pictured, but in 72 games last postseason, HR/Contact leaped to 5.1 percent, which would literally be off the chart.

The HR/Contact rate last August was higher than it had been in any month since August 2009, and the rate last September/October was higher than it had been in any month since August 2004. On the whole, the percentage increase in second-half HR/Contact, relative to first-half HR/Contact, was higher for the 2015 regular season than for any previous season since at least 1950.

Perhaps not surprisingly, the speed of the ball off the bat, as measured by MLB Advanced Media’s tracking system Statcast, also increased late last season. Average exit velocity in September/October was about a mile per hour higher than it had been at its low point in June.

Although this increase in exit velocity helps explain the home runs, it’s still just a symptom of the root reason for the offensive uptick; we’ve substituted one enigma for another. HITf/x data provided by former Mariners special assistant Tony Blengino reveals that no such late-season trend toward higher exit velocities existed in 2013 or 2014, so the 2015 pattern is puzzling.1

The clubhouse theories

After the World Series, we surveyed members of almost every front office to find out how baseball executives accounted for the offensive renaissance in the second half of last season. Three theories predominated: unusually warm weather, which decreases air density and helps batted balls carry; an unprecedented influx of powerful rookie hitters; and a decline in pitching quality stemming from good pitchers being shut down as pennant races resolved themselves early.

Although existing baseball data makes it difficult to analyze the effects of wind and humidity, temperature alone isn’t a satisfactory answer. In-game temperatures were higher during the last two months of the regular season than they were earlier in the season, but Hardball Times writer Jon Roegele found that those extra degrees explained only a small percentage of the rise in scoring. According to physics of baseball researcher Alan Nathan, a 1-degree climb in average temperature would increase home-run rate by only 0.6 percent, so dog-days heat likely had only a modest effect.

The other theories are more persuasive. Last season was an outlier in terms of rookie production, featuring the most productive rookie position players of any year on record. Although many top prospects made productive debuts early in the year, rookie hitters upped their games even further in the second half, when studs such as Miguel Sano, Corey Seager, Francisco Lindor and Carlos Correa did damage immediately. Rookie hitters totaled 155 home runs in August, an all-time record for rookie homers in a single month. And, anecdotally, a number of teams that were out of contention did phone it in on the mound after trades, injuries or innings limits thinned their rotations. The Reds, for one, set a record for consecutive starts by rookie pitchers, with uneven results.

We tried to account for fluctuating talent in two ways. First, we built a model to estimate the exit velocity of each batted ball based on the batter, the pitcher, the temperature, the count, the pitch velocity and the pitch’s called-strike probability. The model assigns a coefficient to each player, derived from actual results; for instance, Zack Greinke reduces estimated exit velocity by 1.5 mph, on average, while Kris Bryant increases it by 3 mph.

Although the model does predict higher exit velocities late in the season, the predicted differences are small, on the order of 0.2 to 0.3 mph. The actual exit velocities exceeded the model’s predictions by 0.13 mph in August, 0.46 mph in September and 0.86 mph in October. And those differences persist even if we limit our sample to full-season hitters and pitchers, which excludes prospects promoted late in the year and replacement-level pitchers who got garbage-time innings for eliminated teams.

As a second check, we compared actual strikeout, walk and home-run rates (per plate appearance) in the second half to the strikeout, walk and home-run rates we would have expected at the All-Star break had we known exactly which batter-pitcher matchups we would see over the rest of the season. To do that, we obtained rest-of-season Steamer projections for every player, generated at the All-Star break, and applied them to the second-half matchups that actually took place (using the odds ratio method). The table below displays the differences between the predicted and actual results.

STAT

PREDICTED

ACTUAL

DIFFERENCE

K%

22.06%

20.43%

-7.40%

BB%

7.13

7.72

+8.30

HR%

2.17

2.84

+30.90

2015 second-half home runs exceeded expectations

Source: FanGraphs

In the second-half matchups, we saw roughly 8 percent more walks and 7 percent fewer strikeouts than Steamer would have expected — modest deviations, perhaps attributable to a league-wide increase in aggressiveness early in the count. Here too, though, the home-run rate stands out: There were 31 percent more home runs hit after the All-Star break than Steamer would have projected, even if it had predicted playing time perfectly. That’s an enormous number, with an astronomically small probability of occurring at random. Even if Steamer had been systematically underrating rookie hitters, it wouldn’t explain these results: In “Return of the Run,” an essay in the latest “Hardball Times Baseball Annual,” Jeff Sullivan calculated that rookies produced only a third of 2015’s increase in home runs, with the rest coming from carryover players.

So: What about the ball?

There’s one factor that we haven’t discussed that a few of the front-office respondents brought up: the baseball. According to an anonymously sourced report by Ken Rosenthal, the league listed “wrapping the ball tighter to make it fly farther” as part of a package of offense-inflating ideas it sent to the MLB Players Association last winter. Although changes in baseball construction have often been advanced as a possible cause of scoring changes over the past few decades, the smoking ball has proved elusive: MLB testing prompted by a rise in home-run rate in the first half of 2000 found negligible differences from 1999 and 1998 balls, and Nathan found no difference in average liveliness between balls from 2004 and the mid-1970s. However, a change in the ball would neatly account for the outcome we’ve observed: a significant increase in exit velocity and home runs, independent of talent and temperature, without a dramatic change in control of the strike zone. According to Nathan, exit speed is most sensitive to ball construction on hard contact, which jibes with our finding that the greatest increase in exit velocity came on line drives. Even more suggestively, the observed exit velocity began to exceed expectations right after the All-Star break:

Some teams order enough balls at the beginning of the year to get them through the first half and then replenish their supplies at the break. If the ball had changed between opening day and midseason, we would expect to see results resembling the line in the chart. The history of clandestine big league baseball-adjusting goes back more than acentury, and there is recent precedent for an unannounced ball change in a high-profile league: Japan’s baseball commissioner resigned in 2013 after news broke that NPB had secretly started using a livelier ball. Of course, there could be an innocent explanation for a change in the ball, since even a minor alteration in materials or manufacturing could produce a significant difference in the ball’s bounciness, or coefficient of restitution (COR).

Major League Baseball’s vice president of communications, Michael Teevan, told us that MLB’s testing has uncovered no evidence of a meaningful change in the baseball. “As a quality control effort, we routinely do testing of baseballs in conjunction with our consultants at UMass-Lowell to ensure that they meet our specifications,” Teevan said. “To this point, we have not uncovered anything suggesting that the balls are related to the increased amount of home runs in the second half.” MLB’s analysis also failed to find a conclusive link between weather and last season’s increase in scoring.

FiveThirtyEight attempted to replicate MLB’s reported results by conducting its own testing using another facility. We purchased a dozen official 2015 postseason baseballs directly from Rawlings and a dozen unopened major league balls manufactured in 2014 from eBay. We sent both sets to the Sports Science Laboratory at Washington State University, where they were stored in an environmental chamber for two weeks to ensure consistent conditions, and then fired from a cannon to strike a fixed cylinder at 95 mph so that their impacts could be measured. The COR of the 2015 balls was only 0.003 higher, on average, which Nathan dismissed as “barely at the accuracy limit of the measurements.” After studying the results, Nathan concluded: “My very definite takeaway from the measurements is that there is no compelling evidence that the balls perform differently.” It’s possible that the newer baseballs have lower seams, which would help them fly farther; the NCAA successfully counteracted a power outage of its own by lowering its regulation ball’s seam height last season. It’s also possible that the balls we tested were in some way not representative of the ones that were used in actual games.2 However, based on both our testing and (according to Teevan) MLB’s, there’s no obvious sign of a disconnect between balls that say “Rob Manfred” and balls that said “Bud Selig.”

The takeaway: Balls were hit harder and cleared fences more often than expected in the second half of last season, even after our best attempts to account for talent and temperature. Because we can’t pinpoint a cause, we can’t say for certain whether 2015’s late-season offense was a misleading blip or a preview of 2016 scoring. This month’s spring-training scores3 suggest we should lean toward the latter: Both home-run rates and overall scoring have returned to their highest spring levels since 2013. Unfortunately, the only way to resolve the uncertainty is to study a larger sample, which means waiting for regular-season baseball to come back — as if we needed another reason to anticipate next week’s opening day.

Footnotes

In addition, there is about a 1 in 10 chance that even if there had been a change in COR large enough to explain the increase in exit velocity, a particular batch of a dozen baseballs would show only a 0.003 increase.